Based on the designed phase shift \(\hat{\mathbf {v}}_l, l=1,\cdots ,L\) , the data symbol is transmitted from the active devices. In this paper, we construct the constellation structure \(\wp \)  according to the tensor decomposition format [1]}. As shown in Fig. REF , it is assumed that the channel use, i.e., \(\tau \) , can be factorized as \(\tau =\Pi _{i}^{d}\tau _i\)  for some \(d\ge 2\)  and \(\tau _i\ge 2, \forall i \) . Subsequently, the complex symbols transmitted by the \(k\) th device at the \(l\) th subblock, denoted by \(\mathbf {s}_{k,l} \in \mathbb {C}^{\tau }\) , can be rewritten as the vector representation of a rank-1 tensor \(\mathcal {S}_{k,l} \in \mathbb {C}^{\tau _1\times \tau _2\times \cdots \times \tau _d}\)  of dimensions \(\tau _1,\tau _2,\cdots ,\tau _d\) , that is
\(\mathbf {s}_{k,l}=\mathrm {vec}(\mathcal {S}_{k,l})\in \mathbb {C}^{\Pi _{i}^{d}\tau _i}=\mathbb {C}^{\tau },\) 
